Our analysis uses phenomenological models to describe the binary black hole population.
The models are calibrated to reproduce the features seen in simulations of globular clusters [1]}.
The fraction of 2G  black holes that are retained in a cluster following a merger depends sensitively upon the spins of 1G  black holes, as larger spins results in larger GW recoil kicks.
Simulations of massive stars with efficient angular momentum transfer predict that black holes would form with spins \(\lesssim 0.01\)  [2]}.
Therefore, our population model also includes the possibility of a fraction of 1G  black holes that have effectively zero spin.
Our analysis demonstrates that this is a potentially key ingredient in the search for hierarchical mergers.
